The major intent of the debate in the Republic is to determine an extended definition of what constitutes Justice in a given state, whether or not a concept of Justice may be determined by citizens in a given state at the time that Plato is writing, and how Justice may be accomplished in a given state (how laws might be enacted that would serve the citizens of a just state in courts of law). Thus it is that the conversation in theRepublic proceeds from a question of meaning (what is Justice?), augmented by questions of fact (are there examples of justice in action or of just men?), to a question of policy (what laws may be effected to ensure the carriage of justice?). Of course if a given state could be founded on a resolution and emulation of such precepts, it would be an ideal state; Plato is generally acknowledged to be an idealistic philosopher.
The argument advanced in this dialogue, then, is an attempt to outline a possible and realistic policy for securing well-being and happy concord (the good life) for the citizens of the state: just citizens dwelling in a just state. The Republic, we are reminded, is translated from a dialogue first written in ancient Greek; perhaps a better translation of its title might be the State, or the Ideal State.
As Plato advances the argument in this dialogue, he sees that he will have to incorporate questions having to do with the education of the ideal citizens; questions having to do with the place of the fictive arts (music, poetry, drama, and so on) in his ideal state, and the philosophies and metaphysics (true knowledge) from which these things ensue.